一类具有无症状感染的随机SEIR传染病模型的平稳分布

The Stationary Distribution of a Stochastic SEIR Infectious Disease Model with Asymptomatic Infections

摘要: 2019年底爆发的新冠疫情截止2023年3月7日，全球累计感染约7.5亿人，累计死亡约686万人，这说明了具有无症状感染的传染病是人类生存与发展的重大威胁之一。因此，本文基于新冠肺炎的传播特点，研究了一类具有无症状感染的随机SEIR传染病模型的平稳分布。首先，通过构建合适的V函数证明了模型正解的存在唯一性。然后，利用Lyapunov方法建立了参数ℜ0s，并且证明了当ℜ0s>1时，模型的解在ℝ+4上存在唯一一个的平稳分布。最后，对本文主要研究内容进行了总结，发现ℜ0s受到白噪声的影响，并且ℜ0s小于等于确定型SEIR模型的基本再生数ℜ0。

Abstract: The COVID-19 broke out at the end of 2019. By March 7, 2023, about 750 million people had been infected and approximately 6.86 million people died in the world. This demonstrates that infectious diseases with asymptomatic infections remain a significant threat to human survival and development. Therefore, based on the transmission characteristics of COVID-19, this paper studies the stationary distribution of the stochastic SEIR infectious diseases model with asymptomatic infection. Firstly, we prove the existence and uniqueness of the positive solution of the model by constructing an appropriate function V. Then, by using the Lyapunov method, we establish the parameterℜ0sand prove that whenℜ0s>1, the solution of the model has a unique stationary distribution inℝ+4. Finally, we summarize the main results of this article and find thatℜ0sis affected by white noise. Furthermore,ℜ0sis less than or equal to the basic reproduction numberℜ0of the deterministic SEIR model.